An Introduction to the Theory of the Cosmic Microwave Background

The accidental1 discovery of the Cosmic Microwave Background radiation by Penzias and Wilson in 1965 started a new era in modern cosmology. The aim of this book is to give a ”not-so-short” introduction into the generation of the observed anisotropy of the Cosmic Microwave Background(CMB). We will discuss the physics involved, and supply analytic calculations of key expressions whenever possible. Moreover, we will derive a semi-analytic approximation to the observed CMB power spectrum, which is usually only available through numerical simulations. Furthermore, we provide a set of python scripts to be able to study the derived expressions.